含变系数或强迫项的KdV方程的新解

付遵涛; 刘式达; 刘式适; 赵强

含变系数或强迫项的KdV方程的新解

北京大学物理学院,北京 100871;2.北京大学湍流与复杂系统研究国家重点实验室,北京 100871

基金项目: 国家自然科学基金(40175016);国家自然科学基金(40035010)

详细信息

作者简介:
付遵涛(1970- )男,黑龙江人,副教授,博士(联系人.Tel:86-10-62767184;E-mail:fuzt@pku.edu.cn).

中图分类号: O175；O411
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出版历程
- 收稿日期: 2002-08-28
- 修回日期: 2003-07-31
- 刊出日期: 2004-01-15

New Exact Solutions to KdV Equations With Variable Coefficients or Forcing

School of Physics, Peking University, Beijing 100871, P. R. China;

摘要

摘要: Jacobi椭圆函数展开法被推广并用于求解另一种形式的KdV方程的新的精确解，所求解的这类KdV方程包括一种典型的变系数的KdV方程和具有强迫项（随机项）的KdV方程．用这种方法得到的新的类周期解在极限条件下可以退化为类孤立波解或类冲击波解．
- Jacobi椭圆函数 /
- 类孤立波解 /
- 类椭圆余弦波解
Abstract: Jacobi elliptic function expansion method is extended to construct the exact solutions to another kind of KdV equations,which have variable coefficients or forcing terms.And new periodic solutions obtained by this method can be reduced to the soliton-typed solutions under the limited condition.
- Jacobi elliptic function /
- soliton-tysped solution /
- cnoidal wave-typed solution

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参考文献(26)

[1]	Grimshaw R H J.Slowly varying solitary waves[J].Proc Roy Soc Lon A, 1979,368(1734):359—375. doi: 10.1098/rspa.1979.0135
[2]	Chan W L，ZHANG Xiao.Symmetries, conservation-laws and Hamiltonian structures of the nonisospectral and variable-coefficient KdV and mKdV equations[J].J Phys A,1995，28(2):407—419. doi: 10.1088/0305-4470/28/2/016
[3]	TIAN Chou.Symmetries and a hierarchy of the general KdV equation[J].J Phys A, 1987,20(2)：359—366. doi: 10.1088/0305-4470/20/2/021
[4]	WANG Ming-liang.Solitary wave solutions for variant Boussinesq equations[J].Phys Lett A,1995,199(3/4):169—172. doi: 10.1016/0375-9601(95)00092-H
[5]	WANG Ming-liang.ZHOU Yu-bin,LI Zhi-bin. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics[J].Phys Lett A, 1996，216(1/5)： 67—75. doi: 10.1016/0375-9601(96)00283-6
[6]	YANG Lei，ZHU Zheng-gang, WANG Ying-hai.Exact solutions of nonlinear equations[J].Phys Lett A, 1999，260(1/2):55—59. doi: 10.1016/S0375-9601(99)00482-X
[7]	YANG Lei,LIU Jiang,YANG Kong-qing.Exact solutions of nonlinear PDE, nonlinear transformations and reduction of nonlinear PDE to a quadrature[J].Phys Lett A, 2001，278(5): 267—270. doi: 10.1016/S0375-9601(00)00778-7
[8]	Parkes E J,Duffy B R.Travelling solitary wave solutions to a compound KdV-Burgers equation[J].Phys Lett A,1997，229(4)：217—220. doi: 10.1016/S0375-9601(97)00193-X
[9]	FAN En-gui.Extended tanh-function method and its applications to nonlinear equations[J].Phys Lett A, 2000,277(45):212—218. doi: 10.1016/S0375-9601(00)00725-8
[10]	Hirota R.Exact N-solutions of the wave equation of long waves in shallow water and in nonlinear lattices[J].J Math Phys,1973,14(7):810—814. doi: 10.1063/1.1666400
[11]	Kudryashov N A.Exact solutions of the generalized Kuramoto-Sivashinsky equation[J].Phys Lett A, 1990,147(5/6):287—291. doi: 10.1016/0375-9601(90)90449-X
[12]	Otwinowski M,Paul R，Laidlaw W G.Exact travelling wave solutions of a class of nonlinear diffusion equations by reduction to a quadrature[J].Phys Lett A,1988,128(9):483—487. doi: 10.1016/0375-9601(88)90880-8
[13]	刘式适，付遵涛，刘式达，等.求某些非线性偏微分方程特解的一个简洁方法[J].应用数学和力学,2001,22(3)：281—286.
[14]	YAN Chun-tao.A simple transformation for nonlinear waves[J].Phys Lett A,1996,224(1/2)：77—84. doi: 10.1016/S0375-9601(96)00770-0
[15]	ZHANG Jie-fang，WU Feng-min.Simple soliton solution method for the (2+1)dimensional long disperive equation[J]. Chinese Physics,1999,8(5)：326—331.
[16]	Porubov A V.Periodical solution to the nonlinear dissipative equation for surface waves in a convecting liquid layer[J].Phys Lett A,1996,221(6)：391—394. doi: 10.1016/0375-9601(96)00598-1
[17]	Porubov A V,Velarde M G.Exact periodic solutions of the complex Ginzburg-Landau equation[J].J Math Phys,1999,40(2)：884—896. doi: 10.1063/1.532692
[18]	Porubov A V,Parker D F. Some general periodic solutions to coupled nonlinear Schrdinger equations[J]. Wave Motion,1999,29(2)：97—108. doi: 10.1016/S0165-2125(98)00033-X
[19]	LIU Shi-kuo,FU Zun-tao,LIU Shi-da,et al.Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations[J].Phys Lett A,2001,289(1/2):69—74. doi: 10.1016/S0375-9601(01)00580-1
[20]	Nirmala N,Vedan M J，Baby B V. Auto-Backland transformation, Lax pairs, Painleve property of a variable coefficient Korteweg-de Vries equation[J].J Math Phys, 1986,27(10):2640—2648. doi: 10.1063/1.527282
[21]	Oevel W H,Steeb W H.Painleve analysis for a time-dependent Kadomtsev-Petviashvili equation[J].Phys A,1984，103(2):239—242.
[22]	Steeb W H,Spicker B M.Kadomtsev-Petviashvili equation with explicit x and t dependence[J].Phys Rev A,1985,31(3):1952—1960. doi: 10.1103/PhysRevA.31.1952
[23]	ZHU Zuo-nong.Lax pairs,Backland transformation, solitary wave solution and infinite conservation laws of the general KP equation and MKP equation with variable coefficients[J]. Phys Lett A,1993,180(6):409—412. doi: 10.1016/0375-9601(93)90291-7
[24]	ZHU Zuo-nong. Painleve property, Backland transformation, Lax pairs and soliton-like solutions for a variable coefficient KP equation[J].Phys Lett A, 1993,182(2/3):277—281. doi: 10.1016/0375-9601(93)91071-C
[25]	Hong W，Jung Y D. Auto-Bckland transformation and analytic solutions for general variable-coefficent KdV equation[J].Phys Lett A,1999,257(3/4):149—152. doi: 10.1016/S0375-9601(99)00322-9
[26]	WANG Ming-liang,WAMG Yue-ming. A new Bckland transformation and multi-solitons to the KdV equations with general variable coefficients[J].Phys Lett A, 2001,287(3/4):211—216. doi: 10.1016/S0375-9601(01)00487-X